I. Field of the Invention
The present invention relates to a linear interpolator for linearly interpolating a staircase waveform signal varying stepwise at a fixed time interval to generate a smooth waveform.
II. Description of the Related Art
It is necessary to convert digital data into analog signals at the final output stage of a measuring instrument such as a digital oscilloscope or a digital function generator, a digital musical instrument, or an audio apparatus such as a compact disk or a digital audio tape recorder. A D/A converter is used to perform such conversion. A signal derived from a D/A converter or the like includes discretely defined staircase waveforms.
It is of critical importance for these apparatuses to transform such discretely defined staircase waveforms into continuous analog waveforms in order to achieve high performance.
FIG. 7 shows an example of a conventional linear interpolating circuit, and FIG. 8 illustrates input and output signal waveforms of various parts of the linear interpolating circuit shown in FIG. 7.
As shown in FIG. 7, the interpolator has a differential amplifier 1, a Miller integrator 2, and a sample-and-hold circuit 3. The differential amplifier 1 receives an input signal from an input terminal 4 at its non-inverting input terminal, and a signal from the sample-and-hold circuit 3 at its inverting input terminal. An output signal from the differential amplifier 1 is applied to the Miller integrator 2, and an output signal from the Miller integrator 2 is fed to an output terminal 5 as an output signal and to the sample-and-hold circuit 3. The sample-and-hold circuit 3 has a capacitor C1, and a switch SW1 which closes only when a sampling pulse SP is applied.
In the linear interpolator thus arranged, the differential amplifier 1 produces a voltage E.sub.R which is the difference between an input signal voltage E.sub.i + applied to input terminal 4 and an input voltage E.sub.i - obtained by sampling-and-holding the output signal at the output terminal 5. Then, the Miller integrator 2 produces an inclined voltage in accordance with the differential voltage E.sub.R, i.e., in accordance with the input signal voltage E.sub.i +, and outputs the inclined voltage as the output voltage E.sub.0 from the output terminal 5.
This linear interpolator, however, has the following problems:
1) As shown in FIGS. 8A-8B, the input signal voltage E.sub.i + comprises a waveform including discrete step-like transitions, and the sampling pulses SP must be well adjusted to be positioned just before the transition (rising and falling edges) of the input signal voltage E.sub.i +, which complicates the circuit design.
2) As shown in FIGS. 8A-8D, a difference 80 between the rising edge of the input signal voltage E.sub.i + and that of the sampling pulse SP distorts the pulse width PW of the differential voltage E.sub.R inputted to the Miller integrator 2.
3) When an input signal comprising a discrete waveform including discrete step-like transitions is supplied from a D/A converter, the input signal may sometimes include distortions 81 such as glitches or overshoots as shown in FIG. 8B. The distortions 81 appear in the output of the differential amplifier 1, which adversely affects the integration carried out by the Miller integrator 2.
4) As a result of 2) and 3) above, it is likely that an error is caused in the slope of the output voltage of the Miller integrator 2 as shown in FIG. 8E. This deteriorates the accuracy of the linear interpolation of the input signal.
5) Complicated circuits such as a differential amplifier and a Miller integrator are required.
6) It is difficult to change the time constant of the Miller integrator 2 because both ends of the resistor R1 and both ends of the capacitor C2 that specify the time constant are not grounded.